Phd Proposal: Procedural, Stochastic, and Fabricable Microstructures


Jonàs Martínez ( and Sylvain Lefebvre (


Alice, INRIA Nancy Grand-Est.


Additive Manufacturing (AM) technologies are now capable of fabricating microstructures at the scale of microns, therefore enabling to precise control of the macroscopic physical behavior. This control empowers a wide range of industrial applications by bringing high-performance customized materials. In particular, a promising venue lies in the optimization of material properties such as rigidity or impact absorption.

Microstructures for AM will play a decisive role in the factory of the future, but several challenges remain aside [1]. The dimension of the objects being printed increases, and concurrently, the available printing resolution becomes finer. Thus, the geometry size of microstructures is drastically escalating. From a computational viewpoint, explicitly storing the microstructure geometry (e.g in an STL file), will eventually render infeasible the whole computational pipeline (numerical simulation, visualization, and computational design of microstructures). From a material science viewpoint, it remains a challenge to properly embed and grade microstructures within an object, and to ensure that they can be directly fabricated with AM processes.

State of the art methods consider periodic microstructures [4, 5, 6], offering compact storage, efficient display, and simulation of the macroscopic physical behavior. However, due to their constrained global structure, periodic microstructures exhibit a poor grading behavior, specially when targeting anisotropic material properties that follow an arbitrary orientation field.

Project description

The objective of the thesis is to tackle the aforementioned  interdisciplinary challenges by considering procedural, stochastic, and fabricable microstructures, with a controlled  macroscopic physical behavior. We have recently contributed novel techniques in this area of research [2, 3].
The detailed description of the PhD proposal can be downloaded from here.

Required qualifications

MSc in computer science.

General information

  • Duration: 3 years.
  • Starting date: 1st September 2018 (or until a suitable candidate
    is found)

Applications to be sent as soon as possible.

How to apply

Send the following documents to in a single ZIP file:

  • CV.
  • A motivation letter describing your interest in this topic.
  • Your degree certificates and transcripts for Bachelor and
    Master (or the last 5 years if not applicable).
  • Master thesis (or equivalent) if it is already completed, or a
    description of the work in progress, otherwise.
  • Publications, if any (it is not expected that you have any).

In addition, at least one recommendation letter from the person who supervises(d) your Master thesis (or research project or  internship) should be sent. At most two other recommendation  letters may be sent. The recommendation letter(s) should be sent  directly by their author to

Help and benefits

  • Monthly net salary of 1600 €. Medical insurance included.
  • Possibility of free French courses.
  • Help for finding housing.
  • Help for the resident card procedure and for husband/wife visa.
  • Lunch cost at INRIA is 2,78 €.


[1] W. Gao and et al., “The status, challenges, and future of additive manufacturing in engineering”, Computer-Aided Design 69 (2015), pp. 65–89.

[2] Jonàs Martínez and Jérémie Dumas and Sylvain Lefebvre, “Procedural Voronoi Foams for Additive Manufacturing”, ACM Transactions on Graphics 35, 4 (2016), pp. 44:1–44:12.

[3] Jonàs Martínez and Haichuan Song and Jérémie Dumas and Sylvain Lefebvre, “Orthotropic k-nearest Foams for Additive Manufacturing”, ACM Transactions on Graphics 36, 4 (2017).

[4] Sigmund, Ole, “Materials with prescribed constitutive parameters: an inverse homogenization problem”, International Journal of Solids and Structures 31, 17 (1994), pp. 2313–2329.

[5] O. Sigmund, “Tailoring materials with prescribed elastic properties”, Mech. Mater. 20, 4 (1995), pp. 351-368.

[6] Sigmund, O and Torquato, S, “Design of Smart Composite Materials Using Topology Optimization”, Smart Materials and Structures 8, 3 (1999), pp. 365.

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